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This actually sparks what I think is an interesting area for discussion. Are there times when it is appropriate to provide an algorithm without explanation?

The “negative times negative is positive” rule is, I think, a reasonable case study. In the US, we tend to introduce operations with negative numbers before we start teaching algebra. When they first encounter multiplication with negative numbers, most students don’t really have the background to understand why two negatives should produce a positive. Is the problem that we are introducing negative numbers too soon? or is it okay to give them a hard-and-fast rule for the short term, with the understanding that, if they continue in mathematics, they will get an explanation? or is there a good way to explain the reasoning behind the rule without resorting to knowledge that they can’t be expected to have?

About MJ4MF

The Math Jokes 4 Mathy Folks blog is an online extension to the book Math Jokes 4 Mathy Folks. The blog contains jokes submitted by readers, new jokes discovered by the author, details about speaking appearances and workshops, and other random bits of information that might be interesting to the strange folks who like math jokes.